Related papers: Defining Root-$T\overline{T}$ operator
This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the…
The article presents a new definition of t-entropy that makes it more explicit and simplifies the process of its calculation.
We consider scalar two-dimensional quantum field theories with the factorizing S-matrix which has poles in the physical strip. In our previous work, we introduced the bound state operators and constructed candidate operators for observables…
We obtain the Baxter Q-operators in the $U_q(\hat{sl}_2)$ invariant integrable models as a special limits of the quantum transfer matrices corresponding to different spins in the auxiliary space both from the functional relations and from…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…
In this paper we present two different problems within the framework of shift-invariant theory. First, we develop a triangular form for shift-preserving operators acting on finitely generated shift-invariant spaces. In case of the normal…
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…
Motivated by quantum field theory (QFT) considerations, we present new representations of the Euler-Beta function and tree-level string theory amplitudes using a new two-channel, local, crossing symmetric dispersion relation. Unlike…
The vacuum expectation values of the so-called Q-operators of certain integrable quantum field theories have recently been identified with spectral determinants of particular Schrodinger operators. In this paper we extend the correspondence…
This paper is our contribution to the study of $T\bar{T}$-deformations. We consider the effect of $T\bar{T}$-deformation of conformal field theories in perturbation theory. We use dimensional regularization scheme to perturbatively…
We investigate the new definition of analytic functional calculus in the terms of representation theory of SL2(R). We avoid any usage of its algebraic homomorphism property and replace it by the demand to be an intertwining operator. The…
Using Hankel operators and shift-invariant subspaces on Hilbert space, this paper develops the theory of the operators associated with soft and hard edges of eigenvalue distributions of random matrices. Tracy and Widom introduced a…
Generally-unbounded infinitesimal generators are studied in the context of operator topology. Beginning with the definition of seminorm, the concept of locally convex topological vector space is introduced as well as the concept of…
One of the major questions in the theory of Toeplitz operators on the Bergman space over the unit disk $\mathbb D$ in the complex plane $\mathbb C$ is a complete description of the commutant of a given Toeplitz operator, that is the set of…
The boundary operator is a linear operator that acts on a collection of high-dimensional binary points (simplices) and maps them to their boundaries. This boundary map is one of the key components in numerous applications, including…
This note aims to present novel positive linear operators involving the Wright function. Furthermore, the present research established the moments of these newly defined operators and estimated the convergence rate using the classical…
In quantum mechanics textbooks the momentum operator is defined in the Cartesian coordinates and rarely the form of the momentum operator in spherical polar coordinates is discussed. Consequently one always generalizes the Cartesian…
In this article, we introduce and study various V-line transforms (VLTs) defined on symmetric 2-tensor fields in $\mathbb{R}^2$. The operators of interest include the longitudinal, transverse, and mixed VLTs, their integral moments, and the…
For quaternionic signal processing algorithms, the gradients of a quaternion-valued function are required for gradient-based methods. Given the non-commutativity of quaternion algebra, the definition of the gradients is non-trivial. The HR…